1. Series and Parallel Circuits

2. Homework
Webassign!

3. Ohm’s law applies for each circuit element and for the circuit as a whole.+ V
Electrons have a choice about which path they follow. A IT R1 R2
V2, I2
V1, I1 V VT
Electrons must all flow in the same path
Series Circuit
Parallel Circuit

4. Electrical Circuits
In a series electric circuit, the voltage drops as it flows through each resistive circuit element

5. Resistors in Series: Building Analogy
R1 = Lamp
6 steps R1
R2 = Lamp
Elevator (battery)
11 steps
R3 = Lamp R2
3 steps
To go from the top to the bottom floor, all people must take the same path. So, by definition, the staircases are in series. With each flight people lose some of the potential energy given to them by the elevator, expending all of it by the time they reach the ground floor. So the sum of the V drops across the resistors the voltage of the battery. People lose more potential energy going down longer flights of stairs, so long stairways correspond to high resistance resistors.
The double waterfall is like a pair of resistors in series because there is only one route for the water to take. The longer the fall, the greater the resistance.

6. Diagramming circuits

7. Kirchoff’s Loop Rule Conservation of Energy
The sum of the changes in potential around any closed path (loop) of a circuit must be zero.

8. Series Circuit Current : One path for the flow of charge
It = I1 = I2 = I3
Resistance must increase because length increases
Rt = R1 + R2 + R3
Voltage must add to Zero
Vt - V1 - V2 - V3=0 Vt =V1 + V2 + V3

9. A V V Name:___________________________________________________ I1 = 1+
V1 = 9
V2 =
R2 = V V

10. V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = Vt = It = Rt = Pt = A V V A V V
Name:___________________________________________________
VT = V1 + V2 + V3 + …
RT = R1 + R2 + R3 + …
IT = I1 = I2 = I3 = …
First, fill in all values of V and I. After review, fill in values of R.
Assume all light bulbs have the same resistance.
I1 = A +
Vt = 4 V V L1
V1 = I1 = R1= P1 =
V2 = I2 = R2 = P2 =
Vt = It = Rt = Pt = A
I2 = 2 L2 V V

11. V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = V3 = I3 = R3 = P3 =
VT = V1 + V2 + V3 + …
RT = R1 + R2 + R3 + …
IT = I1 = I2 = I3 = …
First, fill in all values of V and I. After review, fill in values of R.
Assume all light bulbs have the same resistance.
IT = 1 A +
I2 = V
V2 = 3
R2 =
VT =
I1 = L3 L1 L2
V1 =
I1 =
R1 =
V3 =
I3 =
R3 =
V1 = I1 = R1= P1 =
V2 = I2 = R2 = P2 =
V3 = I3 = R3 = P3 =
Vt = It = Rt = Pt =

12. Series Circuit Example
VT = V1 + V2 + V3 + …
RT = R1 + R2 + R3 + …
IT = I1 = I2 = I3 = …
Series Circuit Example IT A
V1 = I1 = R1= P1 =
V2 = I2 = R2 = P2 =
V3 = I3 = R3 = P3 =
Vt = It = Rt = Pt =
V1 =
I1 =
R1 = 5W + VT V V A
V2 =
I2 = 1A
R2 = V V
Given:
Vt = 10V
R1 = 5W
I2 = 1A
P3 = 2W
V3 =
I3 =
R3 = V V

13. Series Circuit Example
VT = V1 + V2 + V3 + …
RT = R1 + R2 + R3 + …
IT = I1 = I2 = I3 = … IT
Series Circuit Example A
V1 = I1 = R1= P1 =
V2 = I2 = R2 = P2 =
V3 = I3 = R3 = P3 =
Vt = It = Rt = Pt =
V1 =
I1 =
R1 = 5W + VA V V A
V2 =
I2 = 1A
R2 = + VB V V
Given:
VA = 3V
VB = 7V
R1 = 5W
I2 = 1A
P3 = 2W
V3 =
I3 =
R3 = V V

14. V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = V3 = I3 = R3 = P3 =
VT = V1 + V2 + V3 + …
RT = R1 + R2 + R3 + …
IT = I1 = I2 = I3 = … IT
V1 = I1 = R1= P1 =
V2 = I2 = R2 = P2 =
V3 = I3 = R3 = P3 =
V4 = I4 = R4 = P4 =
Vt = It = Rt = Pt = A
V1 =
I1 =
R1 = 1W V V
V2 =
I2 =
R2 = 2W + VT V V A
I5 =
V3 = 6V
I3 =
R3 = 3W V V A
I6 =
V4 =
I4 =
R4 = 4W V V

15. V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = V3 = I3 = R3 = P3 =
VT = V1 + V2 + V3 + …
RT = R1 + R2 + R3 + …
IT = I1 = I2 = I3 = …
It =
V1 = I1 = R1= P1 =
V2 = I2 = R2 = P2 =
V3 = I3 = R3 = P3 =
V4 = I4 = R4 = P4 =
Vt = It = Rt = Pt = A
V1 = 3
I1 =
R1 = V V
V2 =
I2 =
R2 = 2W +
Vt = V V A
I5 =
V3 = 5V
I3 =
R3 = V V A
I6 =
V4 = 4V
I4 =
R4 = 4W V V

16. Questions What happens if we greatly increase the resistance?
When else, besides electricity, do we see things like this?
- Think about the effects on voltage (pressure), current (flow), and resistance (blockage)

21. Tell me about heart bypassess…

22. Tell me about heart bypassess…

23. Parallel Circuit More than one path for the flow of charge
More room for the flow of charge so Resistance goes down
Voltage must stay the same since all sections have the same drop

24. Series and Parallel Circuits
Series: Single Path, high effective resistance a L A
Parallel: Multiple Paths, low effective resistance

25. Voltmeters are parallel to the circuit
Parallel Circuit:
Voltmeters are parallel to the circuit
How do the sum of I1, I2, and I3 relate to IT?
Hint: What is current?
What is it made up of? IT IT
I2 + I3 A I1 R1 R2 R3 V1 V2 V3 V V V V V V A A IT A A

26. Voltmeters are parallel to the circuit
Parallel Circuit:
Voltmeters are parallel to the circuit
IT = I1 + I2 + I3 by
Conservation of charge
(conservation of matter) IT IT
I2 + I3 A I1 R1 R2 R3 V1 V2 V3 V V V V V V A IT

27. Kirchoff’s Junction Rule
Conservation of charge

28. Parallel Equations It = I1 + I2 + I3 + … Vt = V1 = V2 = V3 =
How do we find the equivalent or total resistance?

29. Parallel Equations It = I1 + I2 + I3 + … So
It/Vt = I1/Vt + I2/Vt + I3/Vt …
But
Vt = V1 = V2 = V3 =, implying
It/Vt = I1/V1 + I2/V2 + I3/V3 …
Or, by Ohm’s law,
1/Rt = 1/R1 + 1/R2 + 1/R3 + …

30. Parallel Circuit Rules
VT = V1 = V2 = V3 = …
IT = I1 + I2 + I3 + …
1/RT = 1/R1 + 1/R2 + 1/R3 + …
Start here

31. Now map the current flow for circuit 2
Parallel Circuit:
Follow the current
Now map the current flow for circuit 2 IT A A R4 R5 R6
V2, I2
V3, I3 R1
V1, I1 R2 R3 A IT
Circuit 1
Circuit 2

32. How does circuit 1 differ from circuit 2?
Parallel Circuit:
Follow the current
How does circuit 1 differ from circuit 2? IT A A R4 R5 R6
V2, I2
V3, I3 R1
V1, I1 R2 R3 A IT

33. V V A R1 = 100 Ohms VT = 120V R2 = 200 Ohms V1 = V2 = VT RT = V2, I2IT
IT =
I1 =
I2 =

34. V V A R1 = 100 Ohms VT = 120V R2 = 200 Ohms V1 = R3 = 150 Ohms V2 = VT
RT =
V3 =
V2, I2
V3, I3 V V R1
V1, I1 R2 R3 A IT
IT =
I1 =
I2 =
I3 =

35. V V A R1 = VT = 120V Rwire = 0.067 Ohms R2 = V1 = R3 = V2 = VT RT =
V2, I2
V3, I3 V V R1
V1, I1 R2 R3 A IT
IT =
I1 = 5A
I2 = 5A
Find the equivalent resistance Req of this parallel network
I3 = 5A

36. Parallel Circuit:
Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2W, find the other values associated with this circuit. VT
V2, I2
V3, I3 R1
V1, I1 R2 R3 A IT

37. Parallel Circuit:
Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2W, find the other values associated with this circuit.
Vt= V1= V2= V3=
It = I1= I2= I3=
Rt= R1= R2= R3=
Pt= P1= P2= P3= VT
V2, I2
V3, I3 R1
V1, I1 R2 R3 A IT

38. Parallel Circuit:
Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2W, find the other values associated with this circuit.
Vt= V1= 9 V2=9 V3=9
It = I1= I2=1.97 I3= 4.5
Rt=0.95 R1=3 R2=4.6 R3=2
Pt=85.5 P1= 27 P2=18 P3=40.5 VT
V2, I2
V3, I3 R1
V1, I1 R2 R3 A IT

39. Electrical Power & Ohm’s Law
Volt = Joules / Coulomb
Ampere = Coulomb / second
Watt = Joule / Second
Resistance = Kg m2/(Coulomb * sec2)
Ooops!

40. Power Power is the rate of doing work (Watts) Power = Work / time
Power = Volt * q / t but q/t = I
Electrical Power = Voltage * Current = VI
Electrical Energy = Power * Time = VIt

41. More Electric Energy Equations
P = W/t Watt
P = VI = V2/R =I2R
Electric Energy (W)= Pt = VIt = V2/Rt =I2Rt
Joules for all types of Energy

42. Electrical Power Electrical Power is priced in kWh
One kiloWatt = 1000 Watts
One kWh = One kW for one hour

44. Monthly Service Charge is $18
Central Hudson Variable Costs
$0.047
$0.002
-$0.007
$0.004
$0.001
$0.003
$0.065
$0.014
Total
$0.134

45. per Kwh for all additional Kwhs
Monthly Charges –
(Includes the effect of Schedules 59, 91, & 93)
$6.00
Basic Charge,
plus $
per Kwh for the first
600
Kwhs $
per Kwh for the next
700 $
per Kwh for all additional Kwhs
Example -
If you used
1450
Kwhs of electricity, your bill would be calculated like this:
Basic Charge = x
$41.100
$55.531
150
$13.890
Charge for
$116.52
(franchise fees not included)

46. Calculate your electrical cost
List appliances you use
Estimate wattage
Estimate usage
Calculate cost

47. Homework:
Chapter 23:
Problems:page 488
1-6

48. Electrical Power & Ohm’s Law
Volt = Joules / Coulomb
Ampere = Coulomb / second
Watt = Joule / Second
Resistance = Ohms

49. More Power Problems P. 466: 19, 20, 21-25
Use the simplest form of the equation that matches the givens
Check it with another form if desired

50. Practice Parallel
Homework:
Problems 8-14, ****16

51. Homework:
Page: 465
Problems 1-7

52. Chap 22
Problems:
8-13, 15-20

53. Chapter 22
Problems:
21-25

54. Homework:
Chapter 23:
Problems:page 488
1-6
Discuss 7?

55. Homework:
Chapter 23:
Problems:page 488
1-6

56. Homework
p. 526: 9, 10, 13

57. Homework
Test Corrections
p. 526: 9, 10, 13

58. Homework
p. 465: 8, 10,11,12, 13, 16,17,18